Mowing the lawn can be miserable. If you've ever cut your grass during the summer months in Georgia, you understand. When it's 100 degrees and the air is heavy with humidity, the last thing anyone wants to do is work outside. So why not just let your lawn grow out?
It's a fair question. But ask yourself: Do you want to be the one house in the neighborhood that looks like it's in foreclosure even though it's very much occupied? Maintaining a lawn and yard does have its benefits. You cut down on the insect diversity by limiting weed growth, for one. An insect population can grow exponentially if you aren't careful. But who says you need a traditional lawn, anyway?
On the other hand, why not opt for a creeping flower or no-mow lawn instead of grass? Low-level groundcovers such as thyme, sweet alyssum and lavender offer beauty and don't require the maintenance. A no-mow lawn requires no watering or mowing, and those are two ways to positively impact the environment.
You may want to consider hardscaping. Instead of grass, build a desert or rock scene. Hardscaping requires no maintenance, not to mention you won't have to worry about erosion. The landscape may be hard, but taking care of it won't be.